An Iterative Process for Approximating Subactions

We describe a procedure based on the iteration of an initial function by appropriated operator, acting continuous functions, in order to get fixed point. This point will be calibrated subaction for doubling map circle and Lipschitz potential. study analytical generic properties this process we provide some computational evaluations subactions using discretization circle. The is unique if maximizing probability unique. proceed careful analysis dynamics operator close explain difficulty estimating its asymptotic behavior. show that convergence rate can moments like 1/2 sometimes arbitrarily 1.